Einstein's photoelectric equation, particle nature of light
- If c is the velocity of light in free space, the correct statements about photon among the following are :A. The energy of a photon is E=h.B. The velocity of a photon is c.C. The momentum of a photon, p=h/c.D. In a photon-electron collision, both tot… Answer: 3. A, B, C and D only Key idea: Go through the properties of a photon. A: E=hν . True. B: Speed is c . True. C: p=hν/c=frac hλ . Tru... 1
- The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to: Answer: 3. 1/V The shortest X-ray wavelength occurs when the electron gives all its kinetic energy to one photon: eV=dfrachcλ_min . λ_min=hc... 1
- When two monochromatic lights of frequency, and /2 are incident on a photoelectric metal, their stopping potential becomes V_s/2 and V_s respectively. The threshold frequency for this metal is : Answer: 1. 3/2ν Einstein's equation: eV_s=h(ν-ν₀) , so stopping potential is proportional to (ν-ν₀) . Taking the ratio of the two cases: V_s... 1
- The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600 nm, when it delivers the power of 3.3×10^-3 watt will be : (h = 6.6×10^-34 Js) Answer: 3. 10¹⁶ Key idea: number of photons per second N=P/hc/λ=Pλ/hc . N=dfrac3.3×10⁻³×600×10⁻⁹6.6×10⁻³⁴×3×10⁸=dfrac1.98×10⁻⁹1.98×10⁻²⁵=10¹... 1
- When the light of frequency 2_0 (where _0 is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v_1. When the frequency of the incident radiation is increased to 5_0, the maximum velocity of electrons emi… Answer: 1. 1 : 2 Einstein's equation: K_max=hν-hν₀ . At 2ν₀ : K₁=hν₀ . At 5ν₀ : K₂=4hν₀ . Since K=1/2mv² , v∝sqrt K : v₁/v₂=√(1/4)=1/2 Ratio... 1
- The photoelectric threshold wavelength of silver is 3250×10^-10 m. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536×10^-10 m is :(Given h = 4.14×10^-15 eVs and c = 3×10^8 ms^-1) Answer: Dropped in the official answer key: full marks to every candidate Key idea: 1/2mv²=hc/λ-hc/λ₀ . hc=4.14×10⁻¹⁵×3×10⁸=1242 eV nm. Phot... 1
- Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of… Answer: 3. -3 V Einstein's equation: K_max=hν-φ . 5 eV photon, K_max=2 eV, so φ=3 eV. 6 eV photon: K_max=6-3=3 eV. To stop all electrons the... 1
- When a metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is V/4. The threshold wavelength for the metallic surface i… Answer: 4. 3λ Key idea: eV=hc/λ-hc/λ₀ . eV=hc/λ-φ and eV/4=hc/2λ-φ . Subtracting: 3/4eV=hc/2λ⇒ eV=2hc/3λ . φ=hc/λ-2hc/3λ=hc/3λ , so λ₀=3λ . 1